I have a non-stationary output time-series (oil prices) that is to be forecasted with 20 different input time series. The series are all non-stationary. I am considering two approaches.
Approach 1) Using R's
Here I am stuck on how to adjust for non-stationarity as well as how to consider lags and leads of the covariates. Do I consider differenced versions of the regressors in the
xreg argument? I also want to consider lags and leads. Should I transform the predictors to the lags and lead values and then input them to
xreg? What about the output oil price series - should I difference it too before using it ? However, I need to forecast the non-differenced series.
I read this on R's help somewhere. Step 1: build a linear model,step 2: run
auto.arima on the residuals and finally step 3: build an ARIMA model on the original series with the order (p,d,q) as determined in step 2. My question again is do I difference the series to make them stationary before building the linear model, as well as use lag and lead transformations on the predictors. Again, my interest is in forecasting the untransformed oil price series.